Question: Rewrite as a simplified fraction. ${0.91\overline{5} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 915.5555...\\ 100x &= 91.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 824}$ ${x = \dfrac{824}{900}} $ ${x = \dfrac{206}{225}} $